Image reconstruction generally relates to determining an image from input data. In some cases of interest, the input data is Fourier-space information. For example, in coherent X-ray diffraction microscopy, comprehensive X-ray diffraction data (i.e., Fourier-space data) of an object is taken. Computational methods are then employed to determine a real-space image from this diffraction data. However, this determination is not a straightforward Fourier transform of the Fourier-space data, because the X-ray diffraction data provides only the Fourier magnitude. The Fourier phase information is missing from the diffraction data, and must be inferred during the image reconstruction process. This aspect of image reconstruction is known as the phase retrieval problem. The phase retrieval problem is an inverse problem of determining the real-space image that corresponds to given Fourier-space magnitude data.
Phase retrieval methods often rely on additional constraints to expedite processing. For example, the electron density in a crystal is non-negative, so it is appropriate to impose a condition that the real-space image be non-negative when phase retrieval is performed on crystal X-ray diffraction data. As another example, it is often appropriate to specify a real-space domain, within which the real-space image is constrained to lie, as a phase retrieval constraint.
Although image reconstruction employing phase retrieval techniques has been extensively investigated, some practical problems remain. In particular, it can be time consuming to acquire the necessary Fourier magnitude data. Accordingly, it would be an advance in the art to provide a less data-intensive approach for phase retrieval based image reconstruction.